Integration of Modules II: Exponentials

TL;DR

This paper explores an exponential-based approach to integrating Lie algebra representations into algebraic groups over fields of positive characteristic, focusing on over-restricted representations without considering G-stability.

Contribution

It introduces the concept of over-restricted representations and demonstrates the effectiveness of exponential methods for their integration.

Findings

Exponential approach effectively integrates over-restricted representations.

Over-restricted representations are a new class introduced in this work.

The method does not depend on G-stability considerations.

Abstract

We continue our exploration of various approaches to integration of representations from a Lie algebra $\mbox{Lie} (G)$ to an algebraic group $G$ in positive characteristic. In the present paper we concentrate on an approach exploiting exponentials. This approach works well for over-restricted representations, introduced in this paper, and takes no note of $G$-stability.